All Questions ⁺⁰237783 Questions

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40

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+1309

Geometry

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

AnswerscorrectIy Feb 1, 2025

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32

0

+1309

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

AnswerscorrectIy Feb 1, 2025

Jan 31, 2025

0

30

1

+216

Counting

A standard six-sided die is rolled $7$ times. You are told that among the rolls, there was one $1,$ one $2$, one $3$, one $4$, one $5$, and two $6$s. How many possible sequences of rolls could there have been? (For example, 2, 3, read more ..

BRAlNBOLT Jan 31, 2025

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30

0

+216

Counting

At a meeting, four scientists, two mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if the mathematicians must sit next to each other? (Two seatings are considered equivalent if read more ..

BRAlNBOLT Jan 31, 2025

0

32

0

+216

Counting

Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if all the children are next to each other, and all the adults are next to each other? (Two seatings are considered the same if read more ..

BRAlNBOLT Jan 31, 2025

0

27

1

+823

Algebra

Let a1, a2, a3, ... be an arithmetic sequence. Let Sn denote the sum of the first n terms. If S_5 = 1/5 and S_10 = 1/10, then find S_15.

crimefightingvigiI Jan 31, 2025

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26

1

+823

Algebra

Let a1, a2, a3, ..., a10 be an arithmetic series. If a1 + a3 = -2 and a2 + a4 + a6 = 1, then find a1.

crimefightingvigiI Jan 31, 2025

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32

0

+823

Algebra

Laverne starts counting out loud by 5's. She starts with 2. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 100, Shirley runs screaming from the room. What number does Laverne say that sends read more ..

crimefightingvigiI Jan 31, 2025

0

40

0

+823

Algebra

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

crimefightingvigiI Jan 31, 2025

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45

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+4

I NEED HELP!!!!

Can somone help me!

Ehaten Jan 31, 2025

Jan 30, 2025

0

35

0

+1309

Geometry

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $2,$ and the area of triangle $RSX$ is $2.$ Find the area of trapezoid read more ..

AnswerscorrectIy Jan 30, 2025

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35

0

+1309

Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

AnswerscorrectIy Jan 30, 2025

+1

7

7

2

+5

how to determine shape of conic equation?

from a general conic equation (ax^2+by^2+cx+dy+e), how would I determine whether it is a circle, ellipse, parabola, or hyperbola? i just want to know so i can solve a string of questions with varying equations.

taboo Jan 30, 2025

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20

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+460

Geometry

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

MEMEG0D Jan 30, 2025

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27

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+460

Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

MEMEG0D Jan 30, 2025

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39

0

+4

Algebra

(n(1) + n(0)) * 20.62625

dluc2 Jan 30, 2025

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36

0

+1844

Geometry

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

blackpanther Jan 30, 2025

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28

1

+1844

Geometry

Chords UV, WX, and YZ of a circle are parallel. The distance between chords UV and WX is 1, and the distance between chords WX and YZ is also 1. If UV =6 and YZ = 4, then find WX.

blackpanther Jan 30, 2025

0

32

0

+1844

Geometry

A circle is inscribed in a quarter-circle, as shown below. If the radius of the quarter-circle is $4,$ then find the radius of the circle.

blackpanther Jan 30, 2025

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